Precalculus : Functions and Graphs (9th)

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The Ninth Edition of Swokowski Cole's highly respected precalculus text retains the elements that have made it so popular with instructors and students alike; the time-tested exercise sets feature a variety of applications; its exposition is clear; its uncluttered layout is appealing; and the difficulty level of problems is appropriate and consistent. With these elements the authors succeed in preparing students for calculus. PRECALCULUS: FUNCTIONS AND GRAPHS, 9/e is mathematically sound and has excellent problem sets. In this edition, all of the chapters now include numerous technology inserts and examples with specific keystrokes for the TI-83 Plus and the TI-86, ideal for students who are working with a graphing calculator for the first time. The new design of the text makes the technology inserts easily identifiable, allowing professors to skip them if desired.

List of Graphing Calculator Topics

vii

Preface

ix

Topics from Algebra

1

(134)

Real Numbers

2

(17)

Exponents and Radicals

19

(12)

Algebraic Expressions

31

(16)

Equations

47

(19)

Complex Numbers

66

(7)

Inequalities

73

(13)

Rectangular Coordinate Systems

86

(23)

Lines

109

(26)

Review Exercises

128

(4)

Discussion Exercises

132

(3)

Functions

135

(84)

Definition of Function

136

(17)

Graphs of Functions

153

(16)

Quadratic Functions

169

(15)

Operations on Functions

184

(11)

Inverse Functions

195

(10)

Variation

205

(14)

Review Exercises

212

(5)

Discussion Exercises

217

(2)

Polynomial and Rational Functions

219

(64)

Polynomial Functions of Degree Greater Than 2

220

(11)

Properties of Division

231

(8)

Zeros of Polynomials

239

(14)

Complex and Rational Zeros of Polynomials

253

(8)

Rational Functions

261

(22)

Review Exercises

279

(2)

Discussion Exercises

281

(2)

Exponential and Logarithmic Functions

283

(66)

Exponential Functions

284

(12)

The Natural Exponential Function

296

(10)

Logarithmic Functions

306

(16)

Properties of Logarithms

322

(8)

Exponential and Logarithmic Equations

330

(19)

Review Exercises

343

(3)

Discussion Exercises

346

(3)

The Trigonometric Functions

349

(102)

Angles

350

(11)

Trigonometric Functions of Angles

361

(18)

Trigonometric Functions of Real Numbers

379

(19)

Values of the Trigonometric Functions

398

(8)

Trigonometric Graphs

406

(15)

Additional Trigonometric Graphs

421

(8)

Applied Problems

429

(22)

Review Exercises

442

(7)

Discussion Exercises

449

(2)

Analytic Trigonometry

451

(68)

Verifying Trigonometric Identities

452

(6)

Trigonometric Equations

458

(15)

The Addition and Subtraction Formulas

473

(11)

Multiple-Angle Formulas

484

(10)

Product-to-Sum and Sum-to-Product Formulas

494

(5)

The Inverse Trigonometric Functions

499

(20)

Review Exercises

515

(3)

Discussion Exercises

518

(1)

Applications of Trigonometry

519

(64)

The Law of Sines

520

(10)

The Law of Cosines

530

(9)

Vectors

539

(15)

The Dot Product

554

(11)

Trigonometric Form for Complex Numbers

565

(7)

De Moivre's Theorem and nth Roots of Complex Numbers

572

(11)

Review Exercises

578

(4)

Discussion Exercises

582

(1)

Systems of Equations and Inequalities

583

(96)

Systems of Equations

584

(9)

Systems of Linear Equations in Two Variables

593

(9)

Systems of Inequalities

602

(9)

Linear Programming

611

(9)

Systems of Linear Equations in More Than Two Variables

620

(15)

The Algebra of Matrices

635

(10)

The Inverse of a Matrix

645

(7)

Determinants

652

(7)

Properties of Determinants

659

(8)

Partial Fractions

667

(12)

Review Exercises

673

(3)

Discussion Exercises

676

(3)

Sequences, Series, and Probability

679

(84)

Infinite Sequences and Summation Notation

680

(16)

Arithmetic Sequences

696

(7)

Geometric Sequences

703

(9)

Mathematical Induction

712

(7)

The Binomial Theorem

719

(9)

Permutations

728

(7)

Distinguishable Permutations and Combinations

735

(9)

Probability

744

(19)

Review Exercises

757

(3)

Discussion Exercises

760

(3)

Topics from Analytic Geometry

763

(78)

Parabolas

764

(10)

Ellipses

774

(14)

Hyperbolas

788

(12)

Plane Curves and Parametric Equations

800

(15)

Polar Coordinates

815

(16)

Polar Equations of Conics

831

(10)

Review Exercises

837

(2)

Discussion Exercises

839

(2)

Appendixes

841

I Common Graphs and Their Equations

842

II A Summary of Graph Transformations

844

III Graphs of Trigonometric Functions and Their Inverses

846

IV Values of the Trigonometric Functions of Special Angles on a Unit Circle